Encyclopedia of Microtonal Music Theory

flu

The "Diophantine clarity" division, useful for discussing 5-limit tempering. If one step is a "flu", then a Pythagorean comma is 900 flus and a Didymus comma 825 flus, and therefore a schisma is 75 flus. The flu system is plenty accurate enough while tempering the atom out of the discussion. I recommend it as a replacement for Temperament Units.

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[Joe Monzo, Tonalsoft Encyclopedia of Microtonal Music Theory]

An interval measurement invented by Gene Ward Smith as a replacement for Temperament units. It is especially accurate for giving integer values for 5-limit just intonation and some meantone temperaments; it is not as good for higher-limit rational intonation.

A flu is the logarithmic division of the octave into 46032 equal parts. It is calculated as the 46032nd root of 2 (46032√2, or 2(1/46032) ), with a ratio of approximately 1:1.000015058. It is an irrational number, and is one degree of 46032-edo. The formula for calculating the flu-value of any ratio is:
cents = log10r * [46032 / log102] or cents = log2r * 46032, where r is the ratio.

A flu is:

exactly 125/5754 (= ~0.021724018 = ~1/46 ) of a millioctave

exactly 64/2877 (= ~0.022245395 = ~1/45 ) of a yamaha-unit

exactly 25/959 (= ~0.026068822 = ~1/38 ) of a cent

exactly 1325/5754 (= ~0.230274592 = ~1/4 ) of a türk-sent

exactly 30103/46032 (= ~0.653958116 = ~2/3 ) of a jot

approximately 4/5 (= ~0.800065785) of a temperament-unit

exactly 1 65/959 (= ~1.067778936 = ~1 1/15 ) 12mus (dodekamus)

exactly 260/959 (= ~4.271115746 = ~4 1/4 ) 14mus (tetradekamus)

Here are flu values for some intervals of 5-limit just-intonation and associated temperament measurement units:

It so happens that the generator "5ths" of 1/3-comma meantone, 1/5-comma meantone, and 1/11-comma meantone all come extremely close to an integer flu value. Because 46032 is exactly divisible by 12, all intervals in 12-edo have exact integer flu values. Here are some flu values for "5ths" of some meantone temperaments: